Wave as Disturbance and Signal in a Physics-Informed Framework for Shallow Water Bathymetry

Satellite-derived bathymetry (SDB) commonly treats the sea surface as a source of radiometric disturbance, although the same surface wave field can also contain water depth information through gravity wave propagation. This article presents a Wave-Aware Physics-Informed Neural Network (WA-PINN) that represents these two roles within a unified shallow water bathymetry framework. The optical geometry stream combines Sentinel-2 multispectral observations with seafloor geometry. The disturbance stream converts European Centre for Medium Range Weather Forecasts Reanalysis Version 5 (ERA5) wind forcing into Mean Square Slope (MSS) through the Cox–Munk relationship and introduces a roughness-dependent sunglint contribution into the optical physics constraint. The signal stream retrieves local wavelength, propagation direction, and wave celerity from Sentinel-2 surface texture and constrains predicted depth with the finite depth gravity wave dispersion relation. A Wave Validity Factor (WVF) controls the influence of the dispersion constraint according to the coherence and physical plausibility of the retrieved wave field. The three streams are fused in a shared depth predictor constrained by supervised depth loss, optical physics loss, and wave dispersion physics loss. The framework is demonstrated over Culebra, St. Thomas, and St. John in the northeastern Caribbean Sea. The complete Dual Role model reaches an overall Root Mean Square Error (RMSE) of 1.21 m, a Mean Absolute Error (MAE) 0.77 m, and an R2 of 0.96. Relative to the Slope Aware configuration, the Disturbance and Signal models reduce RMSE by 15.7% and 12.8%, while the complete model reduces RMSE by 29.7%. The disturbance contribution increases under stronger wind forcing, whereas the signal contribution increases with WVF. Depth-dependent RMSE increases from 0.82 m at 0 to 5 m to 1.58 m at 20 to 30 m. These results illustrate the intended complementarity between correcting wave-induced optical contamination and exploiting wave propagation as an additional depth constraint.